NC2 Flashcards
Numerical symbols are an ______ human invention
Arbitrary
(Gobel et al., 2014)
The understanding of numerical symbols is a good predictor of
Later math achievement
(Gobel et al., 2014)
What did Gobel state was a good predictor of later math achievement?
Understanding of numerical symbols
Fuson, 1988
2 year old children can recite the….
Numerical sequence
Fuson, 1988
2 year olds can recite a numerical sequence, but
Haven’t yet understood the numerical meaning
Fuson, 1988
2 year olds can recite a numerical sequence, but haven’t yet understood the numerical meaning.
At this stage, number words are
Like placeholders
English children learn the meaning of a number-word at around
24-36 months
English children learn the meaning of _______ at around 24-36 months
A number word
Cross-linguistic studies have suggested learning the meaning of ‘one’ is easier when
The language has a singular/plural distinction
If a language has a singular/plural distinction, it is
Easier to learn the meaning of one
(Gelman + Gallistel, 1978)
What are the counting principles? (5)
- Stable order
- One-to-one
- Abstraction
- Order irrelevance
- Cardinality
(Gelman + Gallistel, 1978)
What does ‘stable-order’ refer to
Words recited in fixed order
- Stable order
- One-to-one
- Abstraction
- Order irrelevance
- Cardinality
^ These are the __________
Counting principles
(Gelman + Gallistel, 1978)
‘One-to-one’ correspondence refers to
Each object can only be counted once
(Gelman + Gallistel, 1978)
‘Abstraction’ refers to
ANYTHING can be counted (sounds, objects, people)
(Gelman + Gallistel, 1978)
‘Order Irrelevance’ refers to
Knowing the order in which things are counted is irrelevant
(Gelman + Gallistel, 1978)
‘Cardinality’
The LAST pronounced number identifies the number of the set
(Gelman + Gallistel, 1978)
The LAST pronounced number identifies the number of the set
Cardinality
(Gelman + Gallistel, 1978)
Knowing the order in which things are counted is irrelevant
Order irrelevance
(Gelman + Gallistel, 1978)
ANYTHING can be counted (sounds, objects, people)
Abstraction
Abstraction is one of the
Counting principles
Cardinality is one of the
Counting principles
(Wynn, 1990)
The ‘give a number task’ (i.e. 5 tomatoes please’ can help when
Learning to count
(Give a number task –> Developmental stages in the acquisition of cardinality principle)
Pre-number knower
Numerosity given is unrelated to requested number
(Give a number task –> Developmental stages in the acquisition of cardinality principle)
One-knower
Child can accurately give 1
More than 1 for ANY NUMBER higher than 1
(Give a number task –> Developmental stages in the acquisition of cardinality principle)
Two-knower
Incorrect for any number higher than 2
(Give a number task –> Developmental stages in the acquisition of cardinality principle)
three-knower
Incorrect for any number higher than 3
(Give a number task –> Developmental stages in the acquisition of cardinality principle)
Four-knower
Incorrect for any number higher than 4
(Give a number task –> Developmental stages in the acquisition of cardinality principle)
Pre-number knower, one-knower, two-knower, three-knower and four-knowers all make up
Subset-knowers
(Give a number task –> Developmental stages in the acquisition of cardinality principle)
If you are a cardinal principle knower,
Know the exact meaning of all number words
(Give a number task –> Developmental stages in the acquisition of cardinality principle)
A cardinal principle knower knows
The exact meaning of all the number words
Being a Cardinal Principle knower lasts approximately
1 1/2 years
Becoming a cardinal principle knower is a _____ and ________ process
Long
Error prone
Variability in cardinal principle-knowing may be based on (2)
SES
Home numeracy
Cardinal principle knower
Children from high SES backgrounds reach the understanding of cardinality between
34-51 months
Cardinal principle knower
Children from a less privileged background typically reach cardinal understanding at around
48 months
Cardinal principle knower
Who reaches cardinal understanding first - high SES or low SES
High SES
Cardinal principle knower
What is ‘home numeracy’?
Practicing numeracy with parents
(Levine et al., 2010)
Home numeracy: “Number talk” at home predicts
Cardinality knowledge
Two ways in which magnitude representations support children acquisition of meaning of number words? (2)
- Mapping number words to ANS
2. Object tracking system
(Dehaene, 1997)
Mapping of number words to ANS gives number words an approximate numerical meaning. This acts as
Scaffolding to counting acquisition
Children first learn the meaning of small number words by….
Linking them to objects (object tracking system)
What is the object tracking system limit?
3-4
Children learn meaning of small number words by object tracking. For larger numbers, children perform a
induction (conceptual shift) from list to external objects
For larger sets, children perform a induction (conceptual shift) from list to external objects
For example, one more object in the set…
Corresponds to the next number word in the list
Transparent languages reflect
Place-value explicitly
Advantage of learning to count in a transparent language? (2)
- Fewer number words to learn
2. Base-ten system explicitly marked
- Fewer number words to learn
- Base-ten system explicitly marked
^ What language is this?
Transparent language
Sigeler + Mu (2008)
Superior performance of Asian children in mathematics could be explained by
Transparency of the number system
Inversion
Order of number words is reversed, e.g. German
Moyer + Landauer (1978)
Effects in single digit processing: ________
Digit comparison task
Which researchers came up with the Digit Comparison Task?
Moyer + Landauer (1978)
Moyer + Landauer (1978)
Method: Digit Comparison Task
Choose the larger
Moyer + Landauer (1978)
Digit Comparison Task performance is affected by (2)
- Distance effect
2. Size effect
Moyer + Landauer (1978)
Distance effect: the closer
2 digits are in value, the longer it takes to decide which is larger
Moyer + Landauer (1978)
Size effect:
The larger the digits are, the longer it takes to decide which is larger
Moyer + Landauer (1978)
Distance effect + size effect =
Ratio effect
Moyer + Landauer (1978)
The ratio effect provides evidence that
Symbolic number processing is influenced by non-symbolic representations
Size congruity effect, a.k.a
Numerical stroop
Size congruity effect - there is
An incongruency between physical size and numerical size
Numerical Stroop
Longer RTs for…
Incongruent trials
Schneider et al., (2017)
A recent meta-analysis found that symbolic number processing (digit comparison) relates to
Mathematical achievement
Rouselle + Noelle, 2007
Children with math disability show a reduced…
Performance in symbolic digit comparison
